Rational number approximation in higher radix floating point systems

Abstract

Recent research has shown that hybrid non-binary floating point bases, particularly decimal-based systems, can match or exceed the error performance of more traditional binary systems. The authors address a more general question of whether such bases offer any further advantages in the domain of rational number approximation. They consider the effect of the choice of floating point base on rational number approximation in systems which exhibit the typical characteristics of floating point representations, normalized encodings, limited exponent range, and storage allocated in a fixed number of bits per datum. The frequency with which terminating and representable results can be expected is considered for binary, decimal, and other potentially interesting bases (base 30 and base 210).<>